Scalable unstructured mesh algorithms and implementations

Paul Plassmann
Department of Computer Science and Engineering
Penn State

Abstract:
Unstructured meshes are a powerful computational tool used in the
numerical modeling of physical phenomena on complex, irregular domains.
Instead of requiring a uniform distribution of grid points, unstructured
meshes allow grid points to be strategically placed in the computational
domain. Thus, these meshes are particularly effective in modeling
irregular boundaries, multiscale geometries, and rapidly changing
solutions.
The use of these meshes on parallel machines has been limited because
of the number of diverse tasks that must be accomplished in a scalable
manner to use this approach effectively. These tasks include the
generation, adaptive refinement, quality improvement, and partitioning
of the unstructured mesh. In addition, many applications require the
assembly and solution of large, sparse linear systems.
In this talk, we describe new parallel algorithms for these tasks and
discuss the vertical intergration of software for accomplishing these
tasks as part of the SUMAA3d
project. We present a P-RAM analysis showing the scalability of a
strategy based on computation on independent sets. Experimental results
obtained on a diverse set of parallel architectures, including the IBM
SP and ATM-connected networks of workstations, are discussed. Finally,
we compare the parallel performance of the two- and three-dimensional
versions of these algorithms from the point of view of scalability and
computational efficiency.